The goal of this investigation is to determine an equation for the locus of the vertex of a parabola when the linear parameter is varied

Point C is the vertex of the parabola f.
1. Leaving a and c fixed, adjust the slider for b. What shape is traced out by the vertex?
2. Erase the trace by using Ctrl F on your keyboard.
3. Change a and c, and then repeat #1. How do a and c seem to affect the shape traced out by the vertex as b changes?
4. Fix a = 1 and c = -2, and change b. Find the equation of the shape traced out by the vertex. Check your work by graphing your equation.
5. Fix a = -1 and c = 1, and change b. Find the equation of the shape traced out by the vertex. Check your work by graphing your equation.
6. Find the equation for the shape traced out by the vertex when adjusting b for any value of a and c.